Irreducible divisor simplicial complexes

Baeth, Nicholas; Hobson, John

doi:10.2140/involve.2013.6.447

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Irreducible divisor simplicial complexes

Nicholas R. Baeth and John J. Hobson

Vol. 6 (2013), No. 4, 447–460

DOI: 10.2140/involve.2013.6.447

Abstract

For an integral domain $D$ , the irreducible divisor graph $G_{D} (x)$ of a nonunit $x \in D$ gives a visual representation of the factorizations of $x$ . Here we consider a higher-dimensional generalization of this notion, the irreducible divisor simplicial complex $S_{D} (x)$ . We show how this new structure is a true generalization of $G_{D} (x)$ , and show that it often carries more information about the element $x$ and the domain $D$ than its two-dimensional counterpart.

Keywords

factorization, simplicial complex

Mathematical Subject Classification 2010

Primary: 13A05

Secondary: 55U10

Milestones

Received: 6 August 2012

Revised: 12 October 2012

Accepted: 15 October 2012

Published: 8 October 2013

Communicated by Scott Chapman

Authors

Nicholas R. Baeth
Mathematics and Computer Science University of Central Missouri W. C. Morris 213 Warrensburg, MO 64093 United States

John J. Hobson
University of Central Missouri Warrensburg, MO 64093 United States

Vol. 6, No. 4, 2013